Challenge Question:
Wiki says that Egyptian Fractions are distinct unit fractions so e.g. 1/2, 1/3, 1/5 are Egyptian Fractions while 2/4 or 3/9 are not; also you can't repeat the fraction.
Fractions that aren't Egyptian Fractions can be expressed as Egyptian Fractions so, for example, you can have 5/7 = 1/3 + 1/4 + 1/8 + 1/168.
Here's your challenge. Can you express 5/7 as 1/x + 1/y + 1/z where x,y and z are distinct positive integers. If you can't do it, then I'll give the answer myself in about a week.
Have fun.
Moderator edit: This is an approved challenge question.
This problem is inspired by Tony Crilly's book 50 Mathematical Idea. He indicates that it's still unknown how far you can condense Egyptian fractions which people may wish to explore. I'm also wondering whether any (rational) fraction can be expressed as Egyptian Fractions.
Just out of interest how did you compute yours? When I got to my last step I saw my answer immediately but I also realized there could potentially be solutions for...
Spoiler:
Was it just a case of checking through them one by one? Is there a more elegant solution to finding the values?